Simulation of Shallow Solar Pond Batch Water Heaters
B.A. Nigusse* and G.L. Morrison**
**
School of Mechanical and Manufacturing Engineering
The University of New South Wales
Sydney 2052
AUSTRALIA
∗
Engineering College
The University of Asmara
P.O. Box 1220
Asmara, ERITREA
Abstract
The performance of shallow solar pond batch water heaters has been investigated for hot water
production in Sydney, Australia and Asmara, Eritrea. A simulation model was developed to predict the
effect of different design parameters and different modes of operation on the long-term performance of
the heaters. The simulation results indicate that shallow solar pond batch water heaters can be operated
efficiently in multi-draw mode in summer and in single draw mode in winter. These heaters also
perform well for process hot water supply with appropriate selection of pond water depth for a desired
water temperature.
1
INTRODUCTION
Among others, manufacturing and material costs, are the factors that hinder the application of solar hot water systems.
Hence, design of low cost solar water heaters is crucial in harnessing solar energy economically. Shallow solar pond
batch water heaters are low cost solar water heaters that can provide hot water in the range 35 °C to 75 °C. The
proposed design of shallow solar pond batch water heaters is shown in fig 1. This design was proposed by Cohen
(1978), Kudish et al (1978) , Garg et al (1982) and Sodha et al (1980). A typical design consists of a plastic bag with
clear upper layer of 0.2 mm PVF (Tedlar) film and 0.55 mm bottom black film (such as chlorosulfonated polyethylene
or polybutylene) placed in a horizontal tray. The bottom and sidewalls are insulated and the top is covered with either 3
mm ordinary glass or 0.2mm Tedlar film. In this design the insulation should be dense enough to withstand the weight
of the water. The main purpose of the outer glazing in the two-cover design is to suppress heat losses. The choice of
having either glass cover or Tedlar film as outer glazing material is governed by the desired service life and design cost
of the heater. Glass as a cover material has good resistance to abrasion and extreme weather conditions in spite of low
impact strength, high density and poor resistance to thermal stress Blaga (1978). Plastics such as Tedlar have superior
transmission than glass for short wave radiation although it has higher long wave transmission and low strength (Lenel
et al 1984).
Outer Cover
A simulation program was developed based on this
typical design and the forgoing assumptions. The solar
energy after being transmitted through the cover and
water, which absorbs part of the solar radiation, is
absorbed by the back surface. The major portion of the
Insulation
solar energy absorbed by the blackened back surface is
transferred to the water while the rest is transferred
through convection, radiation and conduction to the
surrounding.
The heat loss calculations include
water
Absorber
convection
heat
loss from the outer cover and the
Fig. 1. Schematic diagram of shallow solar
conduction
loss
through
the insulation are related to the
pond batch water heater with glazing
ambient temperature, wind speed and properties and
thickness of insulation. Radiation heat exchange with the sky requires long wave radiation exchange models for clear
and cloudy days, in this simulation program a clear sky radiation exchange model was used to account for the radiation
Inner cover
Simulation of Shallow Solar Pond Batch Water Heaters
B.A. Nigusse and G.L. Morrison
loss. The model can be used to determine the year round performance of the heaters under different operating
conditions for different locations. The proposed design has also been investigated by Tsilingiris (1997) using a semi
empirical model. This model uses an over-all top surface heat loss coefficient calculated from an empirical equation,
including radiation exchange with the sky.
2
SIMULATION MODEL
To simplify the calculations of the transient operation of shallow solar pond batch water heaters the following
assumptions were made:
• Reflection of solar radiation is uniform diffuse in character.
• Solar radiation transmitted through the water body is absorbed completely by the back surface of the water.
• Absorber surface, inner walls of the tank and water are at the same temperature.
The thermal capacity of the plastic absorber and insulation are negligible compared to that of the water mass. The water
surface is in close contact with the inner side of the cover and hence there is no air gap between the water and the inner
cover. Thus, the water is suppressed from evaporation, which otherwise reduces the maximum temperature that can be
achieved. The transmittance absorptance product of the system is calculated using the net radiation method. A
FORTRAN computer program is developed to simulate the performance of the batch solar water heater described
above. The useful energy collected (Qu) is calculated from an energy balance of short wave solar energy input S and the
heat losses from the system. The overall heat loss coefficient is defined in terms of the cover temperature to avoid
program instability due to negative values of radiation loss coefficient at sunrise especially in winter if defined in terms
of ambient temperature.
Qu = AS − AU w (t w − tc 2 ) − ( AU b + AsU s )(t w − ta )
(1)
where Uw (W/m2 K) is the over all heat transfer coefficient from water to the outer cover,
Ub (W/m2 K) is the heat loss coefficient through the bottom insulation and
Us (W/m2 K) is the heat loss coefficient through the side wall insulation.
U w = [1 / (hw + hrw ) + 1 / (hc1 + hr1 )]
(2)
U b = U s = ki / δ
(3)
−1
where hw (W/m2.K) is the convection heat transfer coefficient from the water to the inner cover,
hrw (W/m2.K) is the radiation heat transfer coefficient from the absorber surface to the inner cover,
kI (W/m.K) and δ( m) are thermal conductivity and the thickness of the insulation,
A(m2) is the aperture area of the collector,
As(m2) is the area of the side walls of the collector,
tw, tc2 and ta are the water, outer cover and ambient air temperatures in K.
The heat loss through the bottom and sidewalls of the heater was approximated by the conduction resistance of the
insulation, the convection resistance to the surrounding was considered negligible. The net solar radiation received by
the collector and useful energy collected are given by
S = τα effb I b + τα effd I d
(4)
Qu = Mw Cpw dtw / dt
(5)
where ταeffb and ταeffd are the effective transmittance - absorptance product for beam and diffuse components,
Ib and Id are the beam and diffuse components of solar radiation in W/m2,
Mw is mass of water in the heater (kg) and Cpw (J/kg K) is the specific heat of water.
2
Proceedings of Solar ’97 - Australian and New Zealand Solar Energy Society
Paper 100
Simulation of Shallow Solar Pond Batch Water Heaters
B.A. Nigusse and G.L. Morrison
The inner and outer cover temperatures ( tc1 and tc2 ) were calculated from equations (6) and (7) derived from energy
balances for the covers,
(
)
t c1 = (hw + hrw )t w + (α c1b I b + α c1d I d ) + (hr 1 + hc1 )t c 2 / (hr 1 + hc1 + hw + hrw )
(
)
t c 2 = U w t w + (α c 2b I b + α c 2d I d ) + hc 2 t a − q r 2 / (U w + hc 2 )
(6)
(7)
where αc1and αc2 are the absorptance of the inner and outer cover, respectively,
hr1 (W/m2 K) is the radiation heat transfer coefficient between the two covers,
hc1 (W/m2 K) is the convection heat transfer coefficient between the two covers,
hc2 (W/m2 K) is the convection heat transfer coefficient from the cover to ambient air,
qr2 (W) is the long wave radiation exchange between the outer cover and the sky.
(
qr 2 = ε c 2σ t c 2 − t s
4
4
)
(8)
εc2 is the emittance of the outer cover and ts (K)is temperature of the sky.
The sky temperature is related to the dew point temperature as follows (Duffie 1991),
t s = t a [0.711 + 0.005t dp + 0.000073t a 2 + 0.013 cos(15t m )]1/ 4
(9)
where tdp (K) is the dew point temperature and tm (h) is the hour from midnight.
The energy balance for the system gives the following solution for the rate of change of water temperature tw.


dt w  1
A 

 S − U w (t w − t c1 ) − U b + U s s (t w − t a )
= 
dt  M w Cp w 
A


(10)
The analytical solution of eqn (9) gives the water temperature at the end of the time step and its average value for the
time interval. The average water temperature is used to calculate film heat transfer coefficients.
The effective transmittance - absorptance product of glazed solar pond batch water heaters was calculated using the net
radiation method based on radiation intensity and physical properties of the covers and absorbing surface. The net
radiation method produces a system of linear equations, which can be solved by matrix inversion to get the net radiation
quantity reaching each surface. The individual heat transfer coefficients were calculated using the above eqns and
correlation equations for the thermodynamic properties of water and air. The radiation heat transfer coefficient from the
absorber surface to the inner cover hrw is given by

hrw = σ

 1

1
− 1 (t w 2 + t c1 2 )( t w + t c1 )
 +
 ε a ε c1

(11)
where σ is the Stefan Boltzmann constant, 5.67 x 10-8 W/m2.K4,
εa is emissivity of the absorber and εc1 is emissivity of the inner cover.
The convection heat loss coefficient from the water to the inner cover hw (W/m2 K) is calculated from film heat transfer
equation for heat transfer from the top of a heated horizontal plate
hw = Nuw k w
Lw
(12)
1
Nuw = 0.069 Ra 3 Pr 0.074
Proceedings of Solar ’97 - Australian and New Zealand Solar Energy Society
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Paper 100
3
Simulation of Shallow Solar Pond Batch Water Heaters
B.A. Nigusse and G.L. Morrison
where kw (W/m K) is the thermal conductivity of water, Lw (m) is the pond water depth, Nuw is the Nusselt number for
convection through water (Dropkin et al 1965), Ra is Rayleigh number, and Pr is Prandtl number for the water.
The radiation heat transfer coefficient hr1 (W/m2 K) and convection heat transfer coefficient hc1 (W/m2 K) between the
covers are given by

hr 1 = σ

 1

1
+
− 1 (t c1 2 + t c 2 2 )(t c1 + t c 2 )

 ε c1 ε c 2

hc1 = Nua k a
(14)
La
(15)
where ka (W/m2 K) is the thermal conductivity of air and La (m) is the air gap between the covers. The Nusselt number
for heat transfer through the air gap between two parallel plates as given by Hollands et al (1976) is
1.6
1708  1708( sin 18
. θ) 

. 1 −
Nua = 1 + 144

1 −
Ra cosθ
 Ra cosθ 

+
 Ra cosθ  13 
 − 1


 5830 
+
(16)
where θ is the inclination of the plates to the horizontal. The “+ “ sign indicates that the expression is incorporated only
if it is positive.
The daily useful energy collected (Qud) is calculated from daily tap water temperature and daily maximum water
temperature
Qud = M w Cp w (t wm − t wo )
(17)
The monthly useful energy Qum collected and monthly solar
irradiation Hm is calculated by summing the daily values for the
number of days in each month. The yearly useful energy collected
Quy and yearly solar irradiation Hy and is determined by summing the
monthly values.
CALL DATA
(Reads collector parameter and monthly
water temperature )
CALL INITIAL
( Initializes starting conditions and monthly
3
energy parameter)
COMPUTATION PROCEDURE
The FORTRAN simulation program reads hourly meteorological data
and computes the performance parameters for the water heater. The
computation is performed using a small time step to reduce the error
that can be introduced by assuming that the properties of water are
constant over the computation time step. Then program then
computes the incident angle and the transmittance absorptance
product and the heat transfer coefficients and new water temperature
by iteration. The average water temperature is used to calculate the
heat transfer coefficients. Finally the useful energy, solar irradiation
and useful energy collection efficiency of the system are evaluated.
The computational procedure is given in fig 2.
CALL READ
(Reads hourly weather data)
CALL INITIALD
(Initializes hourly parameters)
CALL ANGLE
CALL TALF
CALL HEATCO
4
RESULTS AND DISCUSSION
To optimise the performance of shallow solar pond batch water
heaters the proposed designs were investigated for glass and Tedlar as
cover materials. In general plastics such as Tedlar, acrylic and Mylar
have higher transmission than glass though they have short service
life, low mechanical strength and high long wave transmission, which
are undesirable properties. The transmittance absorptance product is
CALL TEMP
CALL ENERGYH
(Calculates hourly energy parameter)
NO
Time=hour
YES
Time =End
4
Proceedings of Solar ’97 - Australian and New Zealand Solar Energy Society
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Paper STOP
100
Fig. 2. Shallow solar pond batch water
Simulation of Shallow Solar Pond Batch Water Heaters
B.A. Nigusse and G.L. Morrison
higher for plastic covered heaters than for glass covered heaters. The annual useful energy collection efficiency of a
heater operating in Sydney with a 5 cm pond water depth was found to be 46.5 % and 45.2 % for Tedlar and glass,
respectively. For Asmara it was 44.8 % and 43.6 % for Tedlar and glass, respectively. Tedlar covered heaters show
higher efficiency in both locations. However, the crucial factor in selecting the cover material is not only efficiency of
the heater but also initial cost (which is higher for glass), ease of handling and installation and service life. The prime
target of shallow solar pond batch water heaters being production of hot water at the lowest possible cost, plastics
covers become the appropriate choice of cover material.
4.1
Single daily draw-off operation.
The size of shallow solar pond batch water heaters investigated during simulation was 1.0x1.0 m2 aperture area, 40 mm
cover spacing and various water depths. In order to determine the optimum pond water depth for a specific application
the simulation model was run for a range of pond water depths for Asmara and Sydney weather conditions. The
maximum daily pond water temperature for typical summer and winter days in Asmara is given in figs 3 and 4. The
simulation results indicate that this heater can supply directly useable hot water at about 76 oC in December in Sydney
and 70 oC in March in Asmara for 5 cm pond water depth. The pond water temperature produced in June in Sydney
drops to about 33 oC, which is below the minimum hot water requirement for domestic applications. However, for
Asmara in August and a 5 cm water depth the hot water temperature produced was about 55 oC, which is directly
useable for domestic or other sector applications. Thus, shallow solar pond batch water heaters can be used to supply
hot water through out the year in weather conditions such as Asmara.
The model was also used to predict the grades of hot water produced by categorising the hot water in to temperature
bands and summing up the useful energy collected in the temperature bands. In January and December in Sydney for 5
cm pond water depth 90 % of the hot water delivered was above 60 oC. For Asmara 85 % of the predicted hot water
delivered throughout the year for 5 cm pond water depth was above 60 oC.
4.2
Multiple daily draw-off operation.
Shallow solar pond batch water heaters can be operated in multi draw-off mode at water draw-off temperatures ranging
from 40 oC to 55 oC. The predicted multi draw-off operation of a Tedlar covered heater for 45 oC water draw-off
temperature and 4 cm water depth for Asmara is given in table 2. The results indicate that for 45 oC water temperature
draw-offs can be made from two to three times a day in summer for 4 cm water depth in Sydney. But in winter multi
draw operation is impossible in Sydney. In summer multi draw operation improves the collection efficiency. For
Asmara for water temperature 45 oC and 4 cm pond water depth, draw-offs can be made twice a day through out a year.
Water temperature,
oC
80
w ater depth
15 cm
10 cm
5 cm
60
40
20
0
6
7
8
9
10
11
12
13
14
15
16
17
18
Time(hrs)
Fig 3. Hourly pond water temperature in summer (March 23) for Asmara.
Proceedings of Solar ’97 - Australian and New Zealand Solar Energy Society
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Simulation of Shallow Solar Pond Batch Water Heaters
B.A. Nigusse and G.L. Morrison
Water temperature,
o
C
60
water depth
15 cm
10 cm
5 cm
40
20
0
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Time(hrs)
Fig 4. Hourly pond water temperature in winter (August 31) for Asmara.
Useful energy collected,
MJ/m 2
500
400
300
w ater depth
15 cm
10 cm
5 cm
200
100
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
Fig 5. Monthly useful energy collected in Asmara (Tedlar cover).
Daily average maximum water
temperature, oC
80
60
40
w ater depth
15 cm
10 cm
5 cm
20
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
Fig 6. Monthly daily average maximum water temperature in Asmara (Tedlar cover).
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Proceedings of Solar ’97 - Australian and New Zealand Solar Energy Society
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Simulation of Shallow Solar Pond Batch Water Heaters
B.A. Nigusse and G.L. Morrison
80
Efficiency, %
60
40
water depth
15 cm
10 cm
5 cm
20
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
Fig 7. Monthly solar energy collection efficiency in Asmara (Tedlar cover).
Table 2. Solar irradiation, useful energy collected and efficiency of shallow solar pond batch water heaters
for multi-draw operation mode at 45 oC and 4 cm water depth for Asmara.
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Solar
irradiation
MJ/m2
Qs
698.5
693.1
797.1
781.5
755.8
716.6
641.6
614.4
729.6
749.9
674.4
699.8
Useful energy
MJ/m2
Efficiency,
%
Qu
329.0
308.1
388.9
368.2
346.7
314.8
268.7
248.9
332.8
342.1
293.4
323.8
η
47.1
44.5
48.8
47.1
45.9
43.9
41.9
40.5
45.6
45.6
43.5
46.3
Useful energy
of last draw,
MJ/m2
Qul
86.7
98.4
79.3
80.0
78.9
78.1
76.5
85.5
83.3
94.1
99.8
86.6
Number of
draw-offs
60
58
76
74
72
68
58
50
67
69
57
61
η is monthly useful energy collection efficiency in multi-draw operation mode; and Qul is useful energy collected
from the last draw each day and is not included in the efficiency calculation because the temperature of the last
draw will be less than the required delivery temperature.
4.3
Effect of Insulation and Cover Spacing
The effect of back and side insulation thickness was evaluated for heat loss coefficients (Ub = Us = 0.8 to 2.5 W/m2 K)
corresponding to insulation thickness of approximately 50 to 15 mm. The performance of shallow solar pond batch water
heaters was found to be not significantly effected less by the level of insulation. The solar energy collection efficiency for
Sydney dropped by only 3.1 % and 4.4 % in winter and summer, respectively, when the bottom and side heat loss coefficient
was increased from 0.8 to 2.5 (W/m2 K) for a water depth of 5 cm. Similarly, for 15 cm water depth the efficiency drops by
only 0.23 % and 3.35 % for winter and summer. The drop in efficiency was 3.68 % and 3.92 % for winter and summer,
respectively, for 5 cm pond water depth in Asmara. For 15 cm pond water depth the efficiency dropped by 2.22 % and 2.33 %
for winter and Summer, respectively. These results indicate that insulation thickness of less than 15 mm is required.
Proceedings of Solar ’97 - Australian and New Zealand Solar Energy Society
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Simulation of Shallow Solar Pond Batch Water Heaters
B.A. Nigusse and G.L. Morrison
The effect of cover spacing on the performance of shallow solar pond batch water heater has been investigated using the
simulation model. The results for different cover spacing on a 5 cm deep pond indicate that cover spacing also has only
a minor effect on the heater performance. The useful energy collection improved by about 1.3 % for cover spacing
increase from 4 cm to 12 cm. Thus cover spacing should be no more than 40 mm.
5
CONCLUSIONS
The long term performance of shallow solar pond batch water heaters has been investigated for Sydney and Asmara.
This type solar heater has been shown to be suitable for hot water production for domestic and industrial applications at
low initial capital cost. The following points can be drawn from the simulation results:
1.
Hot water can be produced at temperatures above 70 oC for a pond water depth of 5 cm in summer (December) in
locations such as Sydney however, the performance deteriorates in winter in Sydney. The daily average hot water
temperature for 5 cm water depth in Sydney in June is only 33 oC.
2.
Shallow solar pond batch water heaters perform well in locations like Asmara Eritrea throughout the year. The
highest daily average water temperature produced is 76 oC for a 5 cm pond water depth in Summer (March and
April) and the lowest daily average temperature is 57 oC in August. Thus, the hot water temperature produced by
this type of solar water heater in Asmara in winter can be used directly for domestic applications or as industrial
process feed water.
3.
In multi-draw off operation mode shallow solar pond batch water heaters produce more useful energy than single
draw operation due to reduced heat loss with the multi-draw operation. In summer in Sydney hot water can be
drawn off up to three times a day at 45 oC for water depth of 5 cm. For a required delivery temperature of 50 oC
water can be drawn from two to three times a day for a water depth of 5 cm in summer in Sydney. Shallow solar
pond batch water heaters can not be operated in multi-draw mode in winter in Sydney.
4.
Multi-draw operation of shallow solar pond batch water heaters is possible through out the year for locations such
as Asmara. Hot water can be drawn two times a day at 45 oC for a 4 cm pond water depth in Asmara.
5.
Shallow solar pond batch water heaters with plastic covers perform better than glass covered systems. As plastics
are cheaper than glass it is recommended that shallow solar pond batch water heaters be constructed with a plastic
outer cover.
6.
Side and back heat losses do not significantly effect the performance of shallow solar pond batch water heaters.
The energy collection efficiency drops by only 3.1 % and 4.4 % in winter and summer, respectively when the
bottom and side heat loss coefficient is increased from 0.8 to 2.5 W/m2 K. To determine the optimum insulation
thickness an economic analysis is required.
7.
The performance of shallow solar pond batch water heaters is not significantly effected by cover spacing in the
range of 20 to 40 mm.
8.
Shallow solar pond batch water heaters perform better in locations near the equator since they must be installed
horizontally.
9.
The predicted annual useful energy collection efficiency of shallow solar pond batch water heaters with a Tedlar
cover is 46.5 % and 45.2 % for Sydney and Asmara, respectively.
8
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B.A. Nigusse and G.L. Morrison
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